Journal of Function Spaces http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Input-to-State Stability of Linear Stochastic Functional Differential Equations Thu, 28 Apr 2016 13:59:08 +0000 http://www.hindawi.com/journals/jfs/2016/8901563/ The purpose of the paper is to show how asymptotic properties, first of all stochastic Lyapunov stability, of linear stochastic functional differential equations can be studied via the property of solvability of the equation in certain pairs of spaces of stochastic processes, the property which we call input-to-state stability with respect to these spaces. Input-to-state stability and hence the desired asymptotic properties can be effectively verified by means of a special regularization, also known as “the -method” in the literature. How this framework provides verifiable conditions of different kinds of stochastic stability is shown. Ramazan Kadiev and Arcady Ponosov Copyright © 2016 Ramazan Kadiev and Arcady Ponosov. All rights reserved. Some Extensions of Fixed Point Results over Quasi--Spaces Thu, 28 Apr 2016 12:37:03 +0000 http://www.hindawi.com/journals/jfs/2016/6963041/ We introduce the notion of quasi--metric space. After defining the basic topological properties of quasi--metric space, we investigate fixed point of certain mapping in the frame of complete quasi--metric space. Our results unify and cover several existing fixed point theorems in distinct structures (such as standard quasi-metric spaces, quasi--metric spaces, dislocated quasi-metric spaces, and quasi-modular spaces) in the literature. Maha Noorwali, Hamed H. Alsulami, and Erdal Karapınar Copyright © 2016 Maha Noorwali et al. All rights reserved. Periodic Orbits of Radially Symmetric Keplerian-Like Systems with a Singularity Mon, 18 Apr 2016 14:05:27 +0000 http://www.hindawi.com/journals/jfs/2016/7134135/ We study planar radially symmetric Keplerian-like systems with repulsive singularities near the origin and with some semilinear growth near infinity. By the use of topological degree theory, we prove the existence of two distinct families of periodic orbits; one rotates around the origin with small angular momentum, and the other one rotates around the origin with both large angular momentum and large amplitude. Shengjun Li and Yuming Zhu Copyright © 2016 Shengjun Li and Yuming Zhu. All rights reserved. A Characterization of Symmetric Stable Distributions Sun, 17 Apr 2016 06:57:40 +0000 http://www.hindawi.com/journals/jfs/2016/8384767/ Characterization problems in probability are studied here. Using the characteristic function of an additive convolution we generalize some known characterizations of the normal distribution to stable distributions. More precisely, if a distribution of a linear form depends only on the sum of powers of the certain parameters, then we obtain symmetric stable distributions. Wiktor Ejsmont Copyright © 2016 Wiktor Ejsmont. All rights reserved. Solutions for Impulsive Fractional Differential Equations via Variational Methods Thu, 14 Apr 2016 16:01:34 +0000 http://www.hindawi.com/journals/jfs/2016/2941368/ We investigate the boundary value problems of impulsive fractional order differential equations. First, we obtain the existence of at least one solution by the minimization result of Mawhin and Willem. Then by the variational methods and a very recent critical points theorem of Bonanno and Marano, the existence results of at least triple solutions are established. At last, two examples are offered to demonstrate the application of our main results. Peiluan Li, Hui Wang, and Zheqing Li Copyright © 2016 Peiluan Li et al. All rights reserved. On the Initial Value Problem of Stochastic Evolution Equations in Hilbert Spaces Tue, 12 Apr 2016 09:01:15 +0000 http://www.hindawi.com/journals/jfs/2016/3942707/ The present paper studies the initial value problem of stochastic evolution equations with compact semigroup in real separable Hilbert spaces. The existence of saturated mild solution and global mild solution is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions. The results obtained in this paper improve and extend some related conclusions on this topic. An example is also given to illustrate that our results are valuable. Xuping Zhang, Yongxiang Li, and Pengyu Chen Copyright © 2016 Xuping Zhang et al. All rights reserved. Estimates for Parameter Littlewood-Paley Functions on Nonhomogeneous Metric Measure Spaces Mon, 11 Apr 2016 11:14:12 +0000 http://www.hindawi.com/journals/jfs/2016/9091478/ Let be a metric measure space which satisfies the geometrically doubling measure and the upper doubling measure conditions. In this paper, the authors prove that, under the assumption that the kernel of satisfies a certain Hörmander-type condition, is bounded from Lebesgue spaces to Lebesgue spaces for and is bounded from into . As a corollary, is bounded on for . In addition, the authors also obtain that is bounded from the atomic Hardy space into the Lebesgue space . Guanghui Lu and Shuangping Tao Copyright © 2016 Guanghui Lu and Shuangping Tao. All rights reserved. A Generalization of Uniformly Extremely Convex Banach Spaces Sun, 10 Apr 2016 13:14:23 +0000 http://www.hindawi.com/journals/jfs/2016/9161252/ We discuss a new class of Banach spaces which are the generalization of uniformly extremely convex spaces introduced by Wulede and Ha. We prove that the new class of Banach spaces lies strictly between either the classes of -uniformly rotund spaces and -strongly convex spaces or classes of fully -convex spaces and -strongly convex spaces and has no inclusive relation with the class of locally -uniformly convex spaces. We obtain in addition some characterizations and properties of this new class of Banach spaces. In particular, our results contain the main results of Wulede and Ha. Suyalatu Wulede, Wurichaihu Bai, and Wurina Bao Copyright © 2016 Suyalatu Wulede et al. All rights reserved. Toeplitz Type Operators Associated with Generalized Calderón-Zygmund Operator on Weighted Morrey Spaces Wed, 06 Apr 2016 13:44:44 +0000 http://www.hindawi.com/journals/jfs/2016/8167392/ Let be a generalized Calderón-Zygmund operator or (the identity operator), let and be the linear operators, and let . Denote the Toeplitz type operator by , where and is the fractional integral operator. In this paper, we investigate the boundedness of the operator on weighted Morrey space when belongs to the weighted BMO spaces. Bijun Ren and Enbin Zhang Copyright © 2016 Bijun Ren and Enbin Zhang. All rights reserved. A Fixed Point Approach to the Stability of an Additive-Quadratic-Cubic-Quartic Type Functional Equation Wed, 06 Apr 2016 08:18:21 +0000 http://www.hindawi.com/journals/jfs/2016/8746728/ By applying a fixed point approach, we investigate the stability problems for an AQCQ functional equation of the form Yang-Hi Lee and Soon-Mo Jung Copyright © 2016 Yang-Hi Lee and Soon-Mo Jung. All rights reserved. A Study of Caputo-Hadamard-Type Fractional Differential Equations with Nonlocal Boundary Conditions Wed, 06 Apr 2016 08:12:17 +0000 http://www.hindawi.com/journals/jfs/2016/7057910/ Existence and uniqueness results of positive solutions to nonlinear boundary value problems for Caputo-Hadamard fractional differential equations by using some fixed point theorems are presented. The related Green’s function for the boundary value problem is given, and some useful properties of Green’s function are obtained. Example is presented to illustrate the main results. Wafa Shammakh Copyright © 2016 Wafa Shammakh. All rights reserved. On a Generalization of the Hilbert Frame Generated by the Bilinear Mapping Tue, 05 Apr 2016 09:37:05 +0000 http://www.hindawi.com/journals/jfs/2016/9516839/ The concept of -frame which is a generalization of the frame in Hilbert spaces generated by the bilinear mapping is considered. -frame operator is defined; analogues of some well-known results of frame theory are obtained in Hilbert spaces. Conditions for the existence of -frame in Hilbert spaces are obtained; the relationship between the definite bounded surjective operator and -frame is also studied. The concept of -orthonormal -basis is introduced. Migdad Ismailov, Fatima Guliyeva, and Yusif Nasibov Copyright © 2016 Migdad Ismailov et al. All rights reserved. Weighted Estimates for Toeplitz Operators Related to Pseudodifferential Operators Sun, 03 Apr 2016 14:25:59 +0000 http://www.hindawi.com/journals/jfs/2016/1084859/ The authors establish the weighted estimates for a class of pseudodifferential operators for both cases and , where the weight class is bigger than the classical Muckenhoupt’s weight class. Moreover, the weighted estimates for the Toeplitz operators related to pseudodifferential operators are also obtained. As their special cases, the corresponding results for the commutators of pseudodifferential operators can be deduced. Yan Lin, Zongguang Liu, Chengdan Xu, and Zichu Ren Copyright © 2016 Yan Lin et al. All rights reserved. On the Superstability of Lobačevskiǐ’s Functional Equations with Involution Sun, 03 Apr 2016 13:41:22 +0000 http://www.hindawi.com/journals/jfs/2016/1036094/ Let be a uniquely -divisible commutative group and let and be an involution. In this paper, generalizing the superstability of Lobačevskiǐ’s functional equation, we consider or for all , where . As a direct consequence, we find a weaker condition for the functions satisfying the Lobačevskiǐ functional inequality to be unbounded, which refines the result of Găvrută and shows the behaviors of bounded functions satisfying the inequality. We also give various examples with explicit involutions on Euclidean space. Jaeyoung Chung, Bogeun Lee, and Misuk Ha Copyright © 2016 Jaeyoung Chung et al. All rights reserved. Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation Sun, 03 Apr 2016 09:51:18 +0000 http://www.hindawi.com/journals/jfs/2016/8317567/ This paper deals with the second-order nonlinear neutral delay difference equation , . Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably many positive solutions and the convergence of the sequences generated by the Mann iterative method with errors relative to these solutions for the above equation. Six examples are included. Our results extend and improve essentially the known results in this field. Zeqing Liu, Xin Li, Shin Min Kang, and Young Chel Kwun Copyright © 2016 Zeqing Liu et al. All rights reserved. Discussion on Some Recent Order-Theoretic Metrical Coincidence Theorems Involving Nonlinear Contractions Wed, 30 Mar 2016 08:53:28 +0000 http://www.hindawi.com/journals/jfs/2016/6275367/ We prove some coincidence theorems involving a pair of self-mappings and defined on an ordered metric space wherein is -increasing -contractive mapping. In our results, neither the whole space nor the range subspaces ( or ) are required to be complete. Instead, we use the completeness of a subspace of satisfying suitable conditions. Aftab Alam, Qamrul Haq Khan, and Mohammad Imdad Copyright © 2016 Aftab Alam et al. All rights reserved. Fractional Calculus of Analytic Functions Concerned with Möbius Transformations Tue, 22 Mar 2016 16:00:56 +0000 http://www.hindawi.com/journals/jfs/2016/6086409/ Let be the class of functions in the open unit disk with and . Also, let be a Möbius transformation in for some . Applying the Möbius transformations, we consider some properties of fractional calculus (fractional derivatives and fractional integrals) of . Also, some interesting examples for fractional calculus are given. Nicoleta Breaz, Daniel Breaz, and Shigeyoshi Owa Copyright © 2016 Nicoleta Breaz et al. All rights reserved. On the Hyers-Ulam Stability of First-Order Impulsive Delay Differential Equations Tue, 22 Mar 2016 09:26:25 +0000 http://www.hindawi.com/journals/jfs/2016/8164978/ This paper proves the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of nonlinear first-order ordinary differential equation with single constant delay and finite impulses on a compact interval. Our approach uses abstract Gronwall lemma together with integral inequality of Gronwall type for piecewise continuous functions. Akbar Zada, Shah Faisal, and Yongjin Li Copyright © 2016 Akbar Zada et al. All rights reserved. Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions Sun, 20 Mar 2016 10:00:05 +0000 http://www.hindawi.com/journals/jfs/2016/8107657/ This paper deals with blow-up and global solutions of the following nonlinear reaction-diffusion equations under nonlinear boundary conditions: where is a bounded domain with smooth boundary . We obtain the conditions under which the solutions either exist globally or blow up in a finite time by constructing auxiliary functions and using maximum principles. Moreover, the upper estimates of the “blow-up time,” the “blow-up rate,” and the global solutions are also given. Juntang Ding Copyright © 2016 Juntang Ding. All rights reserved. The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation Wed, 16 Mar 2016 12:39:16 +0000 http://www.hindawi.com/journals/jfs/2016/6814326/ Let be the real unit ball in and . Given a multi-index of nonnegative integers with , we set the quantity where and . In terms of it, we characterize harmonic Bloch and Besov spaces on the real unit ball. This generalizes the main results of Yoneda, 2002, into real harmonic setting. Xi Fu, Zhiyao Xu, and Xiaoyou Liu Copyright © 2016 Xi Fu et al. All rights reserved. On Positive Periodic Solutions to Nonlinear Fifth-Order Differential Equations with Six Parameters Wed, 16 Mar 2016 08:02:28 +0000 http://www.hindawi.com/journals/jfs/2016/8567679/ We study the existence and multiplicity of positive periodic solutions to the nonlinear differential equation: ,  ,  ,  , where ,  , is a 1-periodic function. The proof is based on the Krasnoselskii fixed point theorem. Yunhai Wang and Fanglei Wang Copyright © 2016 Yunhai Wang and Fanglei Wang. All rights reserved. Fast Analytic Sampling Approximation from Cauchy Kernel Tue, 15 Mar 2016 11:33:36 +0000 http://www.hindawi.com/journals/jfs/2016/5780718/ The paper aims at establishing a fast numerical algorithm for , where is any function in the Hardy space and is the scale level. Here, is an approximation to we recently constructed by applying the multiscale transform to the Cauchy kernel. We establish the matrix expression of and find that it has the structure of a multilevel Hankel matrix. Based on the structure, a fast numerical algorithm is established to compute . The computational complexity is given. A numerical experiment is carried out to check the efficiency of our algorithm. Youfa Li, Jing Shang, Honglei Yang, Gengrong Zhang, and Shouzhi Yang Copyright © 2016 Youfa Li et al. All rights reserved. Reiteration Theorems for Two-Parameter Limiting Real Interpolation Methods Sun, 13 Mar 2016 11:26:38 +0000 http://www.hindawi.com/journals/jfs/2016/8214643/ We introduce a limiting real interpolation method involving two scalar parameters. We derive Holmstedt-type estimates for this method that are applied to establish the reiteration theorems. Irshaad Ahmed and Tuba Ejaz Copyright © 2016 Irshaad Ahmed and Tuba Ejaz. All rights reserved. Coefficients Estimates of the Class of Biunivalent Functions Tue, 08 Mar 2016 07:33:40 +0000 http://www.hindawi.com/journals/jfs/2016/3454763/ Applying the Faber polynomial expansions, we obtain the general coefficient bounds for the class of biunivalent functions with bounded boundary rotations. Abdullah Aljouiee and Pranay Goswami Copyright © 2016 Abdullah Aljouiee and Pranay Goswami. All rights reserved. Multilinear Square Functions with Kernels of Dini’s Type Mon, 07 Mar 2016 12:54:52 +0000 http://www.hindawi.com/journals/jfs/2016/4876146/ Let be a multilinear square function with a kernel satisfying Dini(1) condition and let be the corresponding multilinear maximal square function. In this paper, first, we showed that is bounded from to Secondly, we obtained that if each , then and are bounded from to and if there is , then and are bounded from to , where Furthermore, we established the weighted strong and weak type boundedness for and on weighted Morrey type spaces, respectively. Zengyan Si and Qingying Xue Copyright © 2016 Zengyan Si and Qingying Xue. All rights reserved. Products of Composition and Differentiation Operators from Bloch into Spaces Thu, 03 Mar 2016 06:36:50 +0000 http://www.hindawi.com/journals/jfs/2016/5084794/ The boundedness and compactness of the product of differentiation and composition operators from Bloch spaces into spaces are discussed in this paper. Shunlai Wang and Taizhong Zhang Copyright © 2016 Shunlai Wang and Taizhong Zhang. All rights reserved. Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients Wed, 02 Mar 2016 06:56:50 +0000 http://www.hindawi.com/journals/jfs/2016/1391594/ The nonlinear Klein-Gordon equation (KGE) models many nonlinear phenomena. In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE. A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem. Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient. Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly. The numerical results are compared with Lattice Boltzmann Method (LBM). The , , and Root-Mean-Square (RMS) values indicate better accuracy of the proposed method with less computational effort. Nauman Raza, Asma Rashid Butt, and Ahmad Javid Copyright © 2016 Nauman Raza et al. All rights reserved. Some Fixed Point Results for -Type Contractive Mappings Mon, 29 Feb 2016 16:41:34 +0000 http://www.hindawi.com/journals/jfs/2016/1907676/ We prove some fixed point results for new type of contractive mappings using the notion of cyclic admissible mappings in the framework of metric spaces. Our results extend, generalize, and improve some well-known results from literature. Some examples are given to support our main results. Sumit Chandok, Kenan Tas, and Arslan Hojat Ansari Copyright © 2016 Sumit Chandok et al. All rights reserved. About the Existence Results of Fractional Neutral Integrodifferential Inclusions with State-Dependent Delay in Fréchet Spaces Mon, 29 Feb 2016 08:19:08 +0000 http://www.hindawi.com/journals/jfs/2016/6165804/ A recent nonlinear alternative for multivalued contractions in Fréchet spaces thanks to Frigon fixed point theorem consolidated with semigroup theory is utilized to examine the existence results for fractional neutral integrodifferential inclusions (FNIDI) with state-dependent delay (SDD). An example is described to represent the hypothesis. Selvaraj Suganya, Dumitru Baleanu, Siva Selvarasu, and Mani Mallika Arjunan Copyright © 2016 Selvaraj Suganya et al. All rights reserved. Logarithmic Bounds for Oscillatory Singular Integrals on Hardy Spaces Wed, 24 Feb 2016 10:02:48 +0000 http://www.hindawi.com/journals/jfs/2016/1570109/ We establish a logarithmic bound for oscillatory singular integrals with quadratic phases on the Hardy space . The logarithmic rate of growth is the best possible. Hussain Al-Qassem, Leslie Cheng, and Yibiao Pan Copyright © 2016 Hussain Al-Qassem et al. All rights reserved.